SOLUTION: 2 parties each hold 6 people in how many ways can a party of 6 boys and 6 girls divide themselves so that they're equal number of boys and girls in each party?

Algebra ->  Permutations -> SOLUTION: 2 parties each hold 6 people in how many ways can a party of 6 boys and 6 girls divide themselves so that they're equal number of boys and girls in each party?      Log On


   



Question 1012876: 2 parties each hold 6 people in how many ways can a party of 6 boys and 6 girls divide themselves so that they're equal number of boys and girls in each party?
Answer by ikleyn(52779) About Me  (Show Source):
You can put this solution on YOUR website!
.
2 parties each hold 6 people in how many ways can a party of 6 boys and 6 girls divide themselves so that they're equal number of boys and girls in each party?
-----------------------------------------------------------------
You can choose 3 boys of 6 for the first party by C%5B6%5D%5E3 = %286%2A5%2A4%29%2F%281%2A2%2A3%29 = 20 ways.

You can choose 3 girls of 6 for the first party by C%5B6%5D%5E3 = %286%2A5%2A4%29%2F%281%2A2%2A3%29 = 20 ways.

In total, you have 20*20 ways to choose 3 boys of 6 and 3 girls of 6 for the first party. 

The rest of the boys and the girls will participate in the 2nd party without choice.